integral from-pi/2 to pi/2 of xsin(x)

Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} x sin (x) d x

2

Schritte zur Lösung

\int_{- \frac{π}{2}}^{\frac{π}{2}} x sin (x) d x

Wende die partielle Integration an

= [- x cos (x) - \int - cos (x) d x]_{- \frac{π}{2}}^{\frac{π}{2}}

\int - cos (x) d x = - sin (x)

= [- x cos (x) - (- sin (x))]_{- \frac{π}{2}}^{\frac{π}{2}}

Vereinfache

= [- x cos (x) + sin (x)]_{- \frac{π}{2}}^{\frac{π}{2}}

Berechne die Grenzen:

2

= 2

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